Center of Mass, Momentum & Collision

JEE Main level, numerical answer, medium

108 of 130

Question 108 of 130

A particle of mass mm is moving along the xx-axis with initial velocity ui^u\hat{i}. It collides elastically with a particle of mass 10m10m at rest and then moves with half its initial kinetic energy (see figure). If sin⁡θ1=nsin⁡θ2\sin {\theta }_{1}=\sqrt{n}\sin {\theta }_{2} then value of n is ________.

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Answer: 10

From momentum conservation in perpendicular direction of initial motion.
mv1sinθ1=10mv2sinθ2{mv}_{1}{sin\theta }_{1}=10{mv}_{2}{sin\theta }_{2}
Given that (12mu2)12=12mv12…….(2)\left(\dfrac{1}{2}{mu}^{2}\right)\dfrac{1}{2}=\dfrac{1}{2}{mv}_{1}^{2}\ldots \ldots .(2)
From equation (1) & (2)
sinθ1=10sinθ2{sin\theta }_{1}=\sqrt{10}{sin\theta }_{2}
n=10n=10

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